The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female members are not seated together is:

$A$ family consisting of a mother,father,and their $8$ children ($4$ boys and $4$ girls) are to be seated at a round table in a party. How many ways can this be done if the mother and father sit together and the males and females alternate?

Five boys and five girls are to be seated around a circular table. The number of ways in which they can be seated such that no two boys and no two girls are together is:

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is

The number of circular permutations of $n$ different objects is

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is